//
//---------------------  1D  ---------------------
//
//
// Quick is not defined for 1D
//

//
//---------------------  2D  ---------------------
//
//       Staggered Mesh for u-vel and v-vel
//
//   0       1       2       3       4       5   
//
//5      >       >       >       >       > 
//       |       |       |       |       |              
//   ^---+---^---+---^---+---^---+---^---+---^  4       Mesh for scalar fields
//       |       |       |       |       | 
//4      >   o   >   o   >   o   >   o   >               5  x-x-+-x-+-x-+-x-x
//       |       |       |       |       |               4  x o | o | o | o x
//   ^---+---^---+---^---+---^---+---^---+---^  3           +---+---+---+---+
//       |       |       |       |       |               3  x o | o | o | o x
//3      >   o   >   o   >   o   >   o   >                  +---+---+---+---+
//       |       |       |       |       |               2  x o | o | o | o x
//   ^---+---^---+---^---+---^---+---^---+---^  2           +---+---+---+---+
//       |       |       |       |       |               1  x o | o | o | o x
//2      >   o   >   o   >   o   >   o   >               0  x-x-+-x-+-x-+-x-x
//       |       |       |       |       |                  
//   ^---+---^---+---^---+---^---+---^---+---^  1           0 1   2   3   4 5 
//       |       |       |       |       |                 
//1      >   o   >   o   >   o   >   o   >                 o central node
//       |       |       |       |       |                 x boundary node
//   ^---+---^---+---^---+---^---+---^---+---^  0          > u velocity 
//       |       |       |       |       |                 ^ v velocity
//0      >       >       >       >       >    
//       0       1       2       3       4             
//
//                                                  
//          Volumes for u-velocity
//
//   0       1       2       3       4       5
//
//5      >       >       >       >       > 
//       :       :       :       :       :              
//   ^...+---^---+---^---+---^---+---^---+...^  4       Mesh for scalar fields
//       |   |   :   |   :   |   :   |   | 
//4      >   o   >   o   >   o   >   o   >               5  x-x-+-x-+-x-+-x-x
//       |   |   :   |   :   |   :   |   |               4  x o | o | o | o x
//   ^...+---^---+---^---+---^---+---^---+...^  3           +---+---+---+---+
//       |   |   :   |   :   |   :   |   |               3  x o | o | o | o x
//3      >   o   >   o   >   o   >   o   >                  +---+---+---+---+
//       |   |   :   |   :   |   :   |   |               2  x o | o | o | o x
//   ^...+---^---+---^---+---^---+---^---+...^  2           +---+---+---+---+
//       |   |   :   |   :   |   :   |   |               1  x o | o | o | o x
//2      >   o   >   o   >   o   >   o   >               0  x-x-+-x-+-x-+-x-x
//       |   |   :   |   :   |   :   |   |                  
//   ^...+---^---+---^---+---^---+---^---+...^  1           0 1   2   3   4 5 
//       |   |   :   |   :   |   :   |   |                 
//1      >   o   >   o   >   o   >   o   >                 o central node
//       |   |   :   |   :   |   :   |   |                 x boundary node
//   ^...+---^---+---^---+---^---+---^---+...^  0          > u velocity 
//       :       :       :       :       :                 ^ v velocity
//0      >       >       >       >       >    
//
//       0       1       2       3       4              
//
//                       
//                  |           |           |           |
//                --^-----------^-----------^-----------^-- 
//                  |     :     |     :     |     :     |               
//                  |     :     |  (i,j+1)  |     :     |
//                  o     >     o    u_N    o     >     o   
//                  |     :     |     :     |     :     |
//                  |     :     |     :     |     :     |
//                --^---------- 3 -- v_n -- 4 ----------^--  4 = v(i+1, j  )
//                  |     :     |     :     |     :     |    3 = v(i  , j  )
//                  |     :     |     :     |     :     |    2 = v(i+1, j-1)
//                  o    u_W   u_w   u_P   u_e   u_E    o    1 = v(i  , j-1)
//                  |  (i-1,j)  |   (i,j)   |  (i+1,j)  |
//                  |     :     |     :     |     :     |
//                --^---------- 1 -- v_s -- 2 ----------^-- 
//                  |     :     |     :     |     :     |               
//                  |     :     |     :     |     :     |
//                  o     >     o    u_S    o     >     o   
//                  |     :     |  (i,j-1)  |     :     |
//                  |     :     |     :     |     :     |
//                --^-----------^-----------^-----------^--
//                  |           |           |           | 
//                   
//   u_w = ( u(i-1,j) + u(i,j) ) / 2     u_e = ( u(i+1,j) + u(i,j) ) / 2
//   v_n = ( v(i,j) + v(i+1,j) ) / 2     v_s = ( v(i,j-1) + v(i+1,j-1) ) / 2
//              3        4                            1          2          
// 

namespace Tuna {

template<class Tprec, int Dim>
inline bool Quick_XHay<Tprec, Dim>::calcCoefficients2D()
{
    prec_t dy_dx = Gamma * dy / dx;
    prec_t dx_dy = Gamma * dx / dy;
    prec_t dxy_dt = dx * dy / dt;
    prec_t ce, cem, cep, cw, cwm, cwp, CE, CW;
    prec_t cn, cnm, cnp, cs, csm, csp, CN, CS;
    aE = 0.0; aW = 0.0; aN = 0.0; aS = 0.0; aP = 0.0; 
    sp = 0.0;

    for (int i =  bi; i <= ei; ++i)
      for (int j = bj; j <= ej; ++j)
	{
	  CE = ce = ( u(i,j  ) + u(i+1,j  ) ) * 0.5 * dy;
	  CW = cw = ( u(i,j  ) + u(i-1,j  ) ) * 0.5 * dy;
	  CN = cn = ( v(i,j  ) + v(i+1,j  ) ) * 0.5 * dx;
	  CS = cs = ( v(i,j-1) + v(i+1,j-1) ) * 0.5 * dx;
	  cem = cep = 0.0;
	  cwm = cwp = 0.0;
	  cnm = cnp = 0.0;
	  csm = csp = 0.0;
	    
	  // QUICK as presented in Hayase et al. J. of Comput. Phys., 98, 108-118, 1992.
// ---- X
	  if ( ce > 0 ) { 
	    CE = 0;
	    cep = ce * 0.125 * (-phi_0(i-1,j) - 2*phi_0(i,j) + 3*phi_0(i+1,j));
	  } else {
	    if (i == ei) {
	      cem = ce * 0.125 * (-5*phi_0(i+1,j) + 6*phi_0(i,j) - phi_0(i-1,j));
	    } else {
	      cem = ce * 0.125 * (-phi_0(i+2,j) - 2*phi_0(i+1,j) + 3*phi_0(i,j));
	    }
	  }
	  
	  if ( cw > 0 ) {
	    if (i == bi) {
	      cwp = cw * 0.125 * (-5*phi_0(i-1,j) + 6*phi_0(i,j) - phi_0(i+1,j));
	    } else {
	      cwp = cw * 0.125 * (-phi_0(i-2,j) - 2*phi_0(i-1,j) + 3*phi_0(i,j));
	    }
	  } else {
	    CW = 0;
	    cwm = cw * 0.125 * (-phi_0(i+1,j) - 2*phi_0(i,j) + 3*phi_0(i-1,j));
	  }

// ---- Y 
	  if ( cn > 0 ) { 
	    CN = 0;
	    if (j == bj) {
	      cnp = cn * (phi_0(i,j+1) - phi_0(i,j-1)) / 3.0;
	    } else {
	      cnp = cn * 0.125 * (-phi_0(i,j-1) - 2*phi_0(i,j) + 3*phi_0(i,j+1));
	    }
	  } else {
	    if (j == ej-1) {
	      cnm = cn * (phi_0(i,j+2) - phi_0(i,j)) / 3.0;
	    } else if (j < ej-1) {
	      cnm = cn * 0.125 * (-phi_0(i,j+2) - 2*phi_0(i,j+1) + 3*phi_0(i,j));
	    }
	  }
	  
	  if ( cs > 0 ) { 
	    if (j == bj+1) {
	      csp = cs * (phi_0(i,j) - phi_0(i,j-2)) / 3.0;
	    } else if (j > bj+1) {
	      csp = cs * 0.125 * (-phi_0(i,j-2) - 2*phi_0(i,j-1) + 3*phi_0(i,j));
	    }
	  } else {
	    CS = 0;
	    if (j == ej) {
	      csm = cs * (phi_0(i,j-1) - phi_0(i,j+1)) / 3.0;
	    } else {
	      csm = cs * 0.125 * (-phi_0(i,j+1) - 2*phi_0(i,j) + 3*phi_0(i,j-1));
	    }
	  }

	  aE (i,j) = dy_dx - CE;
	  aW (i,j) = dy_dx + CW;
	  aN (i,j) = dx_dy - CN;
	  aS (i,j) = dx_dy + CS;
	  aP (i,j) = aE (i,j) + aW (i,j) + aN (i,j) + aS (i,j) + dxy_dt
	    + (ce - cw) + (cn - cs);

	  sp (i,j) += u(i,j) * dxy_dt - ( p(i+1,j) - p(i,j) ) * dy 
	    - (cep + cem - cwp - cwm + cnp + cnm - csp - csm);	    	   
	}    
    calc_du_2D();
    applyBoundaryConditions2D();
    return 0;
}

//
//---------------------  3D  ---------------------
//

template<class Tprec, int Dim>
inline bool Quick_XHay<Tprec, Dim>::calcCoefficients3D()
{
    prec_t dyz = dy * dz, dyz_dx = Gamma * dyz / dx;
    prec_t dxz = dx * dz, dxz_dy = Gamma * dxz / dy;
    prec_t dxy = dx * dy, dxy_dz = Gamma * dxy / dz;
    prec_t dxyz_dt = dx * dy * dz / dt;
    prec_t ce, cem, cep, cw, cwm, cwp, CE, CW;
    prec_t cn, cnm, cnp, cs, csm, csp, CN, CS;
    prec_t cf, cfm, cfp, cb, cbm, cbp, CF, CB;
    aE = 0.0; aW = 0.0; aN = 0.0; aS = 0.0; aF = 0.0; aB = 0.0; aP = 0.0; 
    sp = 0.0;

    for (int k = bk; k <= ek; ++k)
      for (int i =  bi; i <= ei; ++i)
	for (int j = bj; j <= ej; ++j)
	  {
	    CE = ce = ( u(i+1, j  , k  ) + u(i  ,j  ,k  ) ) * 0.5 * dyz;
	    CW = cw = ( u(i-1, j  , k  ) + u(i  ,j  ,k  ) ) * 0.5 * dyz;
	    CN = cn = ( v(i  , j  , k  ) + v(i+1,j  ,k  ) ) * 0.5 * dxz;
	    CS = cs = ( v(i  , j-1, k  ) + v(i+1,j-1,k  ) ) * 0.5 * dxz;
	    CF = cf = ( w(i  , j  , k  ) + w(i+1,j  ,k  ) ) * 0.5 * dxy;
	    CB = cb = ( w(i  , j  , k-1) + w(i+1,j  ,k-1) ) * 0.5 * dxy;
	    cem = cep = 0.0;
	    cwm = cwp = 0.0;
	    cnm = cnp = 0.0;
	    csm = csp = 0.0;
	    cfm = cfp = 0.0;
	    cbm = cbp = 0.0;
	    
	    // QUICK as presented in Hayase et al.
// ---- X
	    if ( ce > 0 ) { 
	      CE = 0;
	      cep = ce * 0.125 * (-phi_0(i-1,j,k) - 2*phi_0(i,j,k) + 3*phi_0(i+1,j,k));
	    } else {
	      if (i == ei) {
		cem = ce * 0.125 * (-5*phi_0(i+1,j,k) + 6*phi_0(i,j,k) - phi_0(i-1,j,k));
	      } else {
		cem = ce * 0.125 * (-phi_0(i+2,j,k) - 2*phi_0(i+1,j,k) + 3*phi_0(i,j,k));
	      }
	    }
	    
	    if ( cw > 0 ) { 
	      if (i == bi) {
		cwp = cw * 0.125 * (-5*phi_0(i-1,j,k) + 6*phi_0(i,j,k) - phi_0(i+1,j,k));
	      } else {
		cwp = cw * 0.125 * (-phi_0(i-2,j,k) - 2*phi_0(i-1,j,k) + 3*phi_0(i,j,k));
	      }
	    } else {
	      CW = 0;
	      cwm = cw * 0.125 * (-phi_0(i+1,j,k) - 2*phi_0(i,j,k) + 3*phi_0(i-1,j,k));
	    }

// ---- Y 
	    if ( cn > 0 ) { 
	      CN = 0;
	      if (j == bj) {
		cnp = cn * (phi_0(i,j+1,k) - phi_0(i,j-1,k)) / 3.0;
	      } else {
		cnp = cn * 0.125 * (-phi_0(i,j-1,k) - 2*phi_0(i,j,k) + 3*phi_0(i,j+1,k));
	      }
	    } else {
	      if (j == ej-1) {
		cnm = cn * (phi_0(i,j+2,k) - phi_0(i,j,k)) / 3.0;
	      } else if (i < ei-1) {
		cnm = cn * 0.125 * (-phi_0(i,j+2,k) - 2*phi_0(i,j+1,k) + 3*phi_0(i,j,k));
	      }
	    }
	    
	    if ( cs > 0 ) { 
	      if (j == bj+1) {
		csp = cs * (phi_0(i,j,k) - phi_0(i,j-2,k)) / 3.0;
	      } else if (j > bj+1) {
		csp = cs * 0.125 * (-phi_0(i,j-2,k) - 2*phi_0(i,j-1,k) + 3*phi_0(i,j,k));
	      }
	    } else {
	      CS = 0;
	      if (j == ej) {
		csm = cs * (phi_0(i,j-1,k) - phi_0(i,j+1,k)) / 3.0;
	      } else {
		csm = cs * 0.125 * (-phi_0(i,j+1,k) - 2*phi_0(i,j,k) + 3*phi_0(i,j-1,k));
	      }
	    }

// ---- Z 
	    if ( cf > 0 ) { 
	      CF = 0;
	      if (k == bk) {
		cfp = cf * (phi_0(i,j,k+1) - phi_0(i,j,k-1)) / 3.0;
	      } else {
		cfp = cf * 0.125 * (-phi_0(i,j,k-1) - 2*phi_0(i,j,k) + 3*phi_0(i,j,k+1));
	      }
	    } else {
	      if (k == ek-1) {
		cfm = cf * (phi_0(i,j,k+2) - phi_0(i,j,k)) / 3.0;
	      } else if (k < ek-1) {
		cfm = cf * 0.125 * (-phi_0(i,j,k+2) - 2*phi_0(i,j,k+1) + 3*phi_0(i,j,k));
	      }
	    }
	    
	    if ( cb > 0 ) { 
	      if (k == bk+1) {
		cbp = cb * (phi_0(i,j,k) - phi_0(i,j,k-2)) / 3.0;
	      } else if (i > bk+1) {
		cbp = cb * 0.125 * (-phi_0(i,j,k-2) - 2*phi_0(i,j,k-1) + 3*phi_0(i,j,k));
	      }
	    } else {
	      CB = 0;
	      if (k == ek) {
		cbm = cb * (phi_0(i,j,k-1) - phi_0(i,j,k+1)) / 3.0;
	      } else {
		cbm = cb * 0.125 * (-phi_0(i,j,k+1) - 2*phi_0(i,j,k) + 3*phi_0(i,k,k-1));
	      }
	    }

	    aE (i,j,k) = dyz_dx - CE;
	    aW (i,j,k) = dyz_dx + CW;
	    aN (i,j,k) = dxz_dy - CN;
	    aS (i,j,k) = dxz_dy + CS;
	    aF (i,j,k) = dxy_dz - CF;
	    aB (i,j,k) = dxy_dz + CB;
	    aP (i,j,k) = aE (i,j,k) + aW (i,j,k) + 
	      aN (i,j,k) + aS (i,j,k) + aF (i,j,k) + aB (i,j,k) + dxyz_dt
	      + (ce - cw) + (cn - cs) + (cf - cb);
	    
	    sp(i,j,k) = u(i,j,k) * dxyz_dt - 
	      ( p(i+1,j,k) - p(i,j,k) ) * dyz
	      - (cep + cem - cwp - cwm + 
		 cnp + cnm - csp - csm +
		 cfp + cfm - cbp - cbm);
	  }
    calc_du_3D();
    applyBoundaryConditions3D();   
    return 0;
}

} // Tuna namespace













